Quantum mechanics is the study of matter and radiation at an atomic level. It is a mathematical tool for predicting the behaviours of microscopic particles. This chapter discusses the historical background of quantum theory. Planck's idea of discrete energy of a harmonic oscillator implies that the frequencies for the absorbed and emitted radiation should be discrete. According to classical physics, a system can absorb or emit any amount of energy. In 1902 Phillip Edward Anton Von Lenard, an assistant of Hertz, studied photoelectric effect. His setup consisted of a photocell connected to a circuit with a power supply, voltmeter and micro-ammeter. The Franck–Hertz experiment gave an evidence of discrete energy levels of atoms. The particle nature of radiation is established by the Compton effect. Lasers, semiconductors and superconductors are just few among the various applications of the most radical predictions of quantum mechanics.
Quantum mechanics is the study of matter and radiation at an atomic level. It is a mathematical tool for predicting the behaviours of microscopic particles. This chapter discusses the historical background of quantum theory. Planck's idea of discrete energy of a harmonic oscillator implies that the frequencies for the absorbed and emitted radiation should be discrete. According to classical physics, a system can absorb or emit any amount of energy. In 1902 Phillip Edward Anton Von Lenard, an assistant of Hertz, studied photoelectric effect. His setup consisted of a photocell connected to a circuit with a power supply, voltmeter and micro-ammeter. The Franck–Hertz experiment gave an evidence of discrete energy levels of atoms. The particle nature of radiation is established by the Compton effect. Lasers, semiconductors and superconductors are just few among the various applications of the most radical predictions of quantum mechanics.
This chapter examines the historical development of quantum mechanics, focusing on key experiments and theories that challenged classical physics. It begins with blackbody radiation, highlighting the discrepancy between classical predictions and experimental observations, leading to Planck's quantization hypothesis, which posits that energy is emitted in discrete packets (quanta). The chapter covers the photoelectric effect and Compton scattering, demonstrating wave–particle duality and validating quantum theory. It also discusses atomic models, culminating in the Bohr model and the energy-level diagram of the hydrogen atom, which explains atomic phenomena such as line spectra and discrete energy transitions. The chapter concludes by introducing the quantum model, which supersedes the Bohr model by incorporating wave–particle duality and the uncertainty principle, highlighting the necessity of quantum mechanics for accurate atomic-scale descriptions.
Most textbooks say that quantum mechanics came into being when Max Planck, in a desperate attempt to construct a theory that explained experimental data, explored the radical idea of energy being radiated or absorbed by all bodies in discrete packets (or quanta). The energy content of a quantum of radiation is proportional to the frequency of the radiation emitted or absorbed, as in , and the proportionality constant bears the name of Planck. Planck himself was rather uncomfortable with the idea of energy packets, and spent a considerable amount of time in later years trying to “restore” the classical picture of continuous energy exchange between bodies and surroundings. However, in 1905 Einstein was able to use the idea of the quantum to explain the mechanism of the photoelectric effect, which cannot be explained in any other way! This established the reality of the quantum and so, it may be said that Einstein, rather than Planck, is the father of quantum mechanics. Within a few years, Neils Bohr constructed his model of the hydrogen atom in which the electron can only occupy certain special orbits around the nucleus, and any jump between these orbits is accompanied by energy being absorbed or emitted in the form of quanta. The nearly exact agreement of Bohr’s predictions based on the model and observed hydrogen atomic spectra was among the first impressive accomplishments of quantum mechanics.
This chapter starts with the historical development of quantum mechanics and explanations of key concepts behind fundamental discoveries such as Planck's hypothesis, the photoelectric effect, Bohr's atomic model, Compton scattering, the de Broglie hypothesis, the Pauli exclusion principle, the Schrödinger equation, Heisenberg quantum mechanics and the uncertainty principle, the Born interpretation of wave function, the Davisson and Germer experiment, and Dirac relativistic quantum mechanics, which made important contributions to the foundation of modern quantum mechanics. Concepts like the particle properties of radiation, the wave properties of matter, quantized energy and momentum, and the idea that one can no longer know exactly where a single particle like an electron is at any instant of time are brought out clearly through this chapter. A list of important quantum mechanical parameters along with solved examples and unsolved exercises on the key concepts are included towards the end.
Quantum Mechanics and its Interpretations Peter E. Hodgson (bio) Quantum Mechanics is an elegant and indeed beautiful formalism, and enables the results of many physical measurements to be calculated with great accuracy. But from the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything, it is becoming more intense over the years. It should therefore be evident that the most that can be done here is to try to show where the real difficul-ties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. The Discovery of the Quantum The quantum nature of the physical world was discovered by Max Planck in the early years of the twentieth century. He was studying thermodynamics and his attention was drawn to the frequency distribution of black-body radiation. This radiation is emitted from a small hole in a heated enclosure with rough walls, which ensures [End Page 62] that the radiation reaches statistical equilibrium before emission. The frequency distribution is found to be independent of the material lining the walls of the oven, so Planck realized that it must be a fundamental characteristic of all matter. This frequency distribution had been measured by several experimentalists, and Planck resolved to try to see how it can be derived theoretically. Already Rayleigh and Jeans had used classical radiation theory to derive an expression that fitted the data well at low frequencies but tended to infinity at high energies, which was of course unacceptable. The physicist Wien had derived a formula that fitted the data at high frequencies but failed at low frequencies. Planck used an ingenious argument based on entropy to interpolate between these two formulae and obtained a formula, now known as the Planck distribution, that fitted the data perfectly. His next task was to understand the physics behind his formula. He used the familiar technique of assuming that the energy is emitted in small finite amounts, and then let their size tend to zero, so as to represent a continuous distribution. To his great surprise, the intermediate formula with discrete amounts of energy, called quanta, gave the Planck distribution, but the final result, with infinitely small quanta, did not. All his instincts as a physicist rebelled against this conclusion. Surely energy must be emitted continuously. He tried hard to find a way to avoid this unwelcome conclusion, but without success. He had to admit that it is a feature of the world. Soon it was confirmed by Einstein’s interpretation of the photoelectric effect. This story shows clearly that physicists do not impose their ideas on the world, but recognize and accept what they find, whether or not it agrees with their original ideas. The world is made by God in ways that often we cannot imagine. [End Page 63] The Old Quantum Theory A few years later Rutherford discovered that the atom has a small central nucleus containing most of its mass surrounded by a number of electrons. Bohr used the idea of the quantum to build his model of the atom. He assumed that the electrons go around the nucleus in discrete orbits, and that radiation is emitted when an electron falls from one orbit to a lower one. With this model, he was able to calculate to high accuracy the frequencies of the radiation emitted from an excited hydrogen atom. This was a great achievement, but to get his result he had to assume that the electrons stayed in their orbits, whereas classical theory predicted that they would continuously lose energy and rapidly spiral into the nucleus. Quantum Mechanics and its Interpretations These problems were solved by the development of quantum mechanics in the 1920s by Heisenberg, Schrodinger, Dirac, and others. This enabled what is called the wave function to be calculated for any physical system, and from the wave function the probabilities of occurrence of measurable quantities can be found. It is a beautiful theory, and is the indispensable means of calculation for atomic, nuclear...
Abstract This article examines models and theories of energy and matter behaviour developed in microscopic experiments of quantum mechanics; the branch of physics relating to the very small, which studies the physical properties of nature at atomic scales and subatomic particles. It is based on the idea that energy, at the sub-atomic level, can only be emitted and absorbed in discrete amounts - small units – called “quanta”. We begin by remembering that the ideas of the philosopher Democritus, on the assumption of a finite division of matter, led to the search for the atom, allowing the development of what is now known as physics. It is particularly discussed how the understanding of electricity made it possible to affirm and discover the nature of the atom, not as Democritus thought, but that its existence as a basic component of matter could be verified. In this text, we make a path of experiments and ideas that led to the current model of the atom, and that allowed the development of a theory about its nature and properties. Finally, conclusions on this brief study are presented.
This chapter begins by understanding the classical view of an electromagnetic wave and proceed step-by-step in exploring the historical development of quantum mechanics. The frequency of the electromagnetic wave is the same as the frequency of mechanical oscillation of the charge, and the intensity of the electromagnetic wave is the square of the amplitude of the mechanical oscillation of the charge. The origin of quantum mechanics is linked to the discovery of then new laws of radiation by Max Planck in 1900. The explanation of the empirical facts of radiation by Planck using an extraordinarily powerful yet simple model lead to the discovery of the "quantum" nature of radiation. The work to develop a mathematical theory of quantum mechanics continued for a very long time. Two mathematical approaches for the formalism of quantum mechanics emerged. One was developed in 1925 by Werner Heisenberg, called matrix mechanics, and the other was developed by Erwin Schrodinger in 1926 called wave mechanics.